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以向量射影与向量射影定理为理论基础,揭示建立坐标系的奥秘,并找到求轨迹参数方程的通法。例谈计算题、证明题、轨迹题的解法规律。无论哪种题解法的关键,都是根据已有直线垂直关系建立恰当的坐标系,以达到运用代数运算,实现论证几何问题的目的。利用向量射影与向量射影定理,介绍向量在坐标轴上的射影,获得向量在坐标轴上的射影公式,这是平面直角坐标系的基本定理,乃是解析几何发明本质本源之一,它将向量、坐标、三角函数融为一体,应用十分方便。例谈求轨迹参数方程的通法。运用实例阐述《解几辞典》所作改革的探索,概述利用对称、线性代数所取得的进展,末尾建立了在坐标系中确定的正负的定理,既为几何量与其符号化(即坐标系)奠定了理论基础又找到解二元一次不等式的通法。
Based on the theory of vector projection and vector projection, the mystery of establishing coordinate system is revealed, and the general method of finding the parameter equation of trajectory is found out. For example on the calculation, proof, track the law of solution. No matter what kind of problem-solving method is the key, are based on the existing vertical relationship between the vertical line to establish the appropriate coordinate system, in order to achieve the use of algebraic operations to achieve the purpose of demonstration of geometric problems. By using vector projection and vector projective theorem, the vector projection on the coordinate axis is introduced, and the projective formula of vector on the coordinate axis is obtained. This is the basic theorem of planar rectangular coordinate system, which is one of the essential sources of analytic geometry invention. , Coordinates, trigonometric functions into one, the application is very convenient. Example for seeking the path parameter equation method. An example is given to illustrate the exploration of the reform made in the Dictionary of Solutions. The progress made in the use of symmetry and linear algebra is summarized. A positive and negative theorem established in the coordinate system is established at the end of the article. It is not only the relationship between the geometric quantity and its sign (ie, coordinate system) Laid the theoretical foundation and found a solution to the inequality of the binary method.